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Exact solutions of the Lane–Emden-type equation

Authors:	CM Khalique P Ntsime

Institution:	^aInternational Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Post Bag X2046, Mmabatho 2735, South Africa

Abstract:	We classify the Lane–Emden-type equation xy^″+ny^′+x^νf(y)=0 with respect to the standard Lagrangian according to the Noether point symmetries it admits. First integrals of the various cases, which admit Noether point symmetries, and reduction to quadratures for these cases are obtained. Six cases result in new solutions.

Keywords:	Noether point symmetries Lane–Emden equation Isothermal gas sphere Lie group analysis
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